Electromagnetically operated clutches in which permanent magnets are used are known. The permanent magnets are used, for example, for increasing the attraction force on friction faces or to bring about a non-rotationally-fixed transmission of a rotational movement through eddy current induction. Furthermore, permanent magnets in such clutches are also used to fix a certain shifted state of the clutch, for example the engaged clutch, even when the power supply fails, while a second state is brought about by energizing the solenoid, the force of which cancels out the effect of the permanent magnets. It is therefore necessary to maintain at least one of the clutch states predominantly or completely by means of the force applied by the solenoid. For this reason, electromagnetic clutches are considerable consumers of electrical power, for example in vehicles.